Canadian comedy star David Shore thinks British comedy is missing something. "Your standup is the best in the world," he says, "but your improv scene is about 25 years behind us. In LA, you can't meet a single writer or successful actor on a TV show who hasn't at least taken a class at The Groundlings, The Second City or the ImprovOlympic. Every single writer on every show is an improviser." He laughs. "Over here ... well, let's just say you've got the talent. But you don't have the direction."

Shore, who has shared a stage with many of the world's best improvisers, has a point. Improvisational comedy has been the cornerstone of north American comedy since its modern inception in the late 1920s by Viola Spolin, and later the British emigre Keith Johnstone, both inspired by older, improvisational forms of theatre. Spolin's son Paul Sills founded Chicago's famous The Second City club, whose alumni include Bill Murray, Mike Myers, Glee's Jane Lynch and 30 Rock's Tina Fey – in fact, almost every writer and performer ever to grace the stage of Saturday Night Live.

When we think of UK improv, however, little more comes to mind than episodes of Whose Line Is it Anyway?, scenes which, Shore explains, "are funny because they're set up to fail". Although improv lives on in the work of Britain's most successful troupes, Hoopla and Grand Theft Impro, both primarily do shows built up from brief sketches and songs inspired by suggestions from audience.

Shore has greater ambitions. He's in Britain to perform a marathon improvisation form called the Harold, a signature long-form show developed originally in Chicago (the name was cooked up by a San Francisco improv troupe called the Committee, and is a jokey reference to the Beatles film A Hard Day's Night, where George Harrison refers to his haircut as "Arthur" in lieu of anything better). Despite the long form – performances last up to 25 minutes – the Harold has an elaborate structure: from an audience suggestion, a Harold team consisting of five to 10 people performs an opening that inspires a series of scenes and group games. As it progresses, characters from different scenes begin to interact and storylines start to come together. Unlike traditional British improv, which often employs a restrictive narrative arc, anything can happen – and, thanks to Shore, it often does.

Shore is the only person in the UK currently teaching the form, and his waiting list is overflowing with comics such as Abandoman's genius improvising rapper Rob Broderick (seen on BBC's Dick and Dom), Sara Pascoe (The Increasingly Poor Decisions of Todd Margaret, The Thick of It) and several members of sketch artists The Beta Males Picnic.

"Short-form theatre games are fun, but the real skill – where it really gets interesting – is in long-form improv," Shore explains. "That's where you see people inventing an entire show based on one audience suggestion. Everything that comes out your mouth will open a door, and to go through any of those doors will move the scene forward. To create a different Harold show every night from just a word – that's a challenge. That's terrifying."

Shore, 43, grew up in suburban Toronto and began working in standup at the age of 17, but was put off, he says, by the bitterness of the touring comics he met. He moved to LA and started taking classes at the ImprovOlympic, in the hope of starting an improv troupe. It was there that he met Neil Flynn, creator of the famed improvisers Beer Shark Mice (but more commonly known as the Janitor from American TV's Scrubs), before finally moving back to Toronto and joining Second City in 2001 and first experimenting with long-form improv.

Most impressive of all, despite being directed by Mighty Boosh star Rich Fulcher, Shore will perform the Harold alone – the first person ever to do so professionally in Canada, and the only person ever to do it in the UK. It's a challenge, he admits. "I play every single character and it's pretty exhausting. Especially if you do what I do, and accidentally make yourself play a 92-year-old man who spends the next two hours doubled over."

He's also planning on bringing his award-winning long-form improvised talk show MonkeyToast, in which three celebrity interviews provide the basis for an hour-long improv show (past players include Colin Mochrie of Whose Line Is it Anyway?).

Shore's evangelism for improv is obviously paying off in his adopted home: the lineup for Monkey Toast UK will include several of his better-known students, and for the first time in Edinburgh festival history, this year's Fringe will play host to a Harold performance in A Good Improv Show, organised by his graduating students, with a rotating cast and guest starring Shore himself.

"The only complaint in my classes from students is that there's nowhere for them to go see one, to know how it should be done." He smiles wryly. "But by next year, that's going to change."

•A Good Improv Show will be playing at the Sin Club and Lounge, Edinburgh, from 6-27 August 2011 at 1.45pm.